We give some examples to illustrate that scale invariance may not be a manifestation of complex behavior in one-dimensional sandpile models. The multiscaling statistical properties and the existence of intrinsic length scales observed in the local limited one-dimensional model reflects a certain level of complexity. The local, limited, and limited to no traps model presents scale invariance due to the inhomogeneous way of perturbing the lattice. It behaves, however, as the trivial one-dimensional version of the Bak, Tang, and Wisenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] model. A nonlocal limited model presents scaling statistical properties and displays the same level of complexity as the nontrivial two-dimensional models.

• Received 12 July 1996

DOI:https://doi.org/10.1103/PhysRevE.55.2159